Sir Keir Starmer has pitched Labour as the “party of change” as he set his sights on the general election after Labour’s resounding victory over the SNP in the Rutherglen and Hamilton West by-election.

The Labour leader said his party “blew the doors off” in the Scottish contest, marking a “big step in the right direction” on his path to Number 10.

Labour’s higher-than-expected 20.4 percentage point swing from the SNP led analysts to believe that it could return to being the largest party north of the border and open the door to Downing Street if it is replicated at the next national poll.

Speaking at a victory rally alongside Scottish Labour leader Anas Sarwar and winning Labour candidate Michael Shanks, Sir Keir said to applause: “They said that we couldn’t change the Labour Party and we did it.

“They said that we couldn’t win in the south of England and the north of England, and we did it. They said ‘you’ll never beat the SNP in Scotland’ and Rutherglen, you did it. You blew the doors off!”

Sir Keir, whose party is riding high in the national polls, said voters had “turned their back” on the Tory Government.

“But they also not so long ago saw a Labour Party that had drifted away from them.

“We’ve changed. And because we’ve changed, we are now the party of change here in Scotland. We’re the party of change in Britain, we’re the party of change right across the whole country.”

Speaking to journalists, Sir Keir said Rutherglen and Hamilton West, which is representative of central Scotland constituencies that used to be Labour heartlands before being won by the SNP, was a “must-win for us”.

“It was a big step in the right direction, an important one,” he said, adding that “the route to a Labour election win at the next general election runs through Scotland”.

Labour candidate Mr Shanks secured 17,845 votes, well ahead of the 8,399 votes returned for his closest rival, the SNP’s Katy Loudon.

After gaining more than 58% of the votes cast, Mr Shanks has a majority of 9,446.

With Mr Shanks, Labour has two MPs in Scotland – far off its more than 40 in 2010 before its representation collapsed after the 2014 independence referendum.

But the result is being seen as a change in the Scottish political weather and a path to a Labour majority in the House of Commons.

It confirms Labour poses “a serious challenge” to the SNP’s primacy at Westminster and has a momentum comparable with the run-up to the party’s 1997 landslide, according to polling expert Professor Sir John Curtice.

“That potentially has implications for the overall outcome in the general election because if that were to happen, they would find it easier to get an overall majority,” he told the PA news agency.

Pollster Mark Diffley also said Scottish Labour’s apparent revival will make Sir Keir’s job of winning power “much easier”.

Mr Sarwar said his party is “back on the pitch”.

It was 32 points behind the SNP when he became leader, he told Good Morning Scotland, adding: “For us two years on to win a parliamentary by-election for the first time in more than 12 years in Scotland, to get more than double the vote share of the SNP and to get a swing of more than 20%, is seismic, it is huge, it is significant.”

The by-election victory provides Sir Keir with a huge boost days before the party gathers for its autumn conference in Liverpool.

The result will pile more pressure on SNP leader and Scottish First Minister Humza Yousaf – who has seen his party’s fortunes decline in the polls in the wake of the ongoing police investigation into SNP finances.

Mr Yousaf stressed during the election campaign that his party was facing “some very difficult circumstances”, but afterwards acknowledged it had been a “disappointing night” for the SNP.

SNP Westminster leader Stephen Flynn said his party cannot carry on with “business as usual” in light of its defeat.

A total of 30,531 votes were cast in the by-election, with turnout standing at 37.2% – well below the 66.5% turnout in the last general election.

The Scottish Conservatives came in third place, with all candidates bar Labour’s and the SNP’s losing their deposits.

The by-election was called after a recall petition against Margaret Ferrier, who had won the seat for the SNP in 2019 with a majority of 5,230.

Ms Ferrier however had the SNP whip removed after breaching Covid rules in 2020, and after remaining as an independent MP was suspended from the House of Commons, resulting in the recall petition.